CF390E.Inna and Large Sweet Matrix

Inna loves sweets very much. That's why she wants to play the "Sweet Matrix" game with Dima and Sereja. But Sereja is a large person, so the game proved small for him. Sereja suggested playing the "Large Sweet Matrix" game.

The "Large Sweet Matrix" playing field is an n × m matrix. Let's number the rows of the matrix from 1 to n, and the columns — from 1 to m. Let's denote the cell in the i-th row and j-th column as (i, j). Each cell of the matrix can contain multiple candies, initially all cells are empty. The game goes in w moves, during each move one of the two following events occurs:

1. Sereja chooses five integers _x_1, _y_1, _x_2, _y_2, v (_x_1 ≤ _x_2, _y_1 ≤ _y_2) and adds v candies to each matrix cell (i, j) (_x_1 ≤ i ≤ _x_2; _y_1 ≤ j ≤ _y_2).
2. Sereja chooses four integers _x_1, _y_1, _x_2, _y_2 (_x_1 ≤ _x_2, _y_1 ≤ _y_2). Then he asks Dima to calculate the total number of candies in cells (i, j) (_x_1 ≤ i ≤ _x_2; _y_1 ≤ j ≤ _y_2) and he asks Inna to calculate the total number of candies in the cells of matrix (p, q), which meet the following logical criteria: (p < _x_1 OR p > _x_2) AND (q < _y_1 OR q > _y_2). Finally, Sereja asks to write down the difference between the number Dima has calculated and the number Inna has calculated (D - I).

Unfortunately, Sereja's matrix is really huge. That's why Inna and Dima aren't coping with the calculating. Help them!

茵娜非常喜欢糖果。因此，她想和迪马以及谢列亚一起玩“甜蜜矩阵”游戏。但谢列亚体型庞大，结果发现这个游戏对他来说太小了。于是谢列亚提议玩“大型甜蜜矩阵”游戏。

“大型甜蜜矩阵”的游戏场地是一个 $n \times m$ 的矩阵。我们将矩阵的行编号为 $1$ 到 $n$，列编号为 $1$ 到 $m$。记第 $i$ 行、第 $j$ 列的单元格为 $(i,\,j)$。矩阵中每个单元格可存放多个糖果，初始时所有单元格均为空。游戏共进行 $w$ 轮，在每一轮中，发生以下两种事件之一：

1. 谢列亚选择五个整数 $x_1,\,y_1,\,x_2,\,y_2,\,v$（满足 $x_1 \le x_2$，$y_1 \le y_2$），并向矩阵中所有满足 $(i,\,j)$（其中 $x_1 \le i \le x_2$ 且 $y_1 \le j \le y_2$）的单元格各添加 $v$ 颗糖果。
2. 谢列亚选择四个整数 $x_1,\,y_1,\,x_2,\,y_2$（满足 $x_1 \le x_2$，$y_1 \le y_2$）。接着他要求迪马计算所有满足 $(i,\,j)$（其中 $x_1 \le i \le x_2$ 且 $y_1 \le j \le y_2$）的单元格中糖果总数；同时要求茵娜计算矩阵中所有满足如下逻辑条件的单元格 $(p,\,q)$ 中的糖果总数：$(p < x_1\ \text{OR}\ p > x_2)\ \text{AND}\ (q < y_1\ \text{OR}\ q > y_2)$。最后，谢列亚要求写出迪马所得结果与茵娜所得结果之差（即 $D - I$）。

不幸的是，谢列亚的矩阵真的非常巨大，因此茵娜和迪马无法完成这些计算。请帮助他们！

The first line of the input contains three integers n, m and w (3 ≤ n, m ≤ 4·106; 1 ≤ w ≤ 105).

The next w lines describe the moves that were made in the game.

• A line that describes an event of the first type contains 6 integers: 0, _x_1, _y_1, _x_2, _y_2 and v (1 ≤ _x_1 ≤ _x_2 ≤ n; 1 ≤ _y_1 ≤ _y_2 ≤ m; 1 ≤ v ≤ 109).
• A line that describes an event of the second type contains 5 integers: 1, _x_1, _y_1, _x_2, _y_2 (2 ≤ _x_1 ≤ _x_2 ≤ n - 1; 2 ≤ _y_1 ≤ _y_2 ≤ m - 1).

It is guaranteed that the second type move occurs at least once. It is guaranteed that a single operation will not add more than 109 candies.

Be careful, the constraints are very large, so please use optimal data structures. Max-tests will be in pretests.

输入的第一行包含三个整数 $n$、$m$ 和 $w$（$3 \leq n,\,m \leq 4\cdot10^6$；$1 \leq w \leq 10^5$）。

接下来的 $w$ 行描述了游戏中进行的操作。

• 描述第一类事件的一行包含 6 个整数：0、$x_1$、$y_1$、$x_2$、$y_2$ 和 $v$（$1 \leq x_1 \leq x_2 \leq n$；$1 \leq y_1 \leq y_2 \leq m$；$1 \leq v \leq 10^9$）。
• 描述第二类事件的一行包含 5 个整数：1、$x_1$、$y_1$、$x_2$、$y_2$（$2 \leq x_1 \leq x_2 \leq n - 1$；$2 \leq y_1 \leq y_2 \leq m - 1$）。

保证至少会出现一次第二类操作。保证单次操作增加的糖果总数不超过 $10^9$。

请注意，约束条件非常大，因此请使用最优的数据结构。最大规模的测试用例将包含在预测试中。

For each second type move print a single integer on a single line — the difference between Dima and Inna's numbers.

对于每种第二类操作，在单独一行输出一个整数——即迪马的数字与因娜的数字之差。

Note to the sample. After the first query the matrix looks as:

22200
22200
00000
00000

After the second one it is:

22200
25500
03300
00000

After the third one it is:

22201
25501
03301
00001

For the fourth query, Dima's sum equals 5 + 0 + 3 + 0 = 8 and Inna's sum equals 4 + 1 + 0 + 1 = 6. The answer to the query equals 8 - 6 = 2. For the fifth query, Dima's sum equals 0 and Inna's sum equals 18 + 2 + 0 + 1 = 21. The answer to the query is 0 - 21 = -21.

样例说明：第一次查询后，矩阵变为：

22200
22200
00000
00000

第二次查询后，矩阵变为：

22200
25500
03300
00000

第三次查询后，矩阵变为：

22201
25501
03301
00001

对于第四次查询，Dima 的和为 $5 + 0 + 3 + 0 = 8$，Inna 的和为 $4 + 1 + 0 + 1 = 6$。该查询的答案为 $8 - 6 = 2$。对于第五次查询，Dima 的和为 $0$，Inna 的和为 $18 + 2 + 0 + 1 = 21$。该查询的答案为 $0 - 21 = -21$。